Interaction of Gardner solitons in plasmas: applications in the Saturn's magnetosphere

Multi-soliton solutions of the Gardner equation (GE) have been obtained using the Hirota's bilinear formalism and, to the best of our knowledge, have been studied in the context of plasmas for the first time. The results have been used to study the electrostatic waves on the ion time scale in a two-electron temperature (TET) kappa distributed plasma in the light of the data obtained from Saturn's Magnetosphere. The most important result that has come out of the investigation of multi-soliton solution of GE is that both overtaking and head on interactions may occur owing to the simultaneous presence of quadratic and cubic nonlinearities in the GE. The plasma parameters of the system have been found to influence the spatial scale of interaction. The results of kappa distributed plasma have been compared with the Maxwellian case and the key differences with regard to the parametric regimes for the existence of ion acoustic Gardner solitons and the soliton interaction for the two cases have also been explored in detail.